%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SWX217-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:45:36 PM UTC 2026
% Result : Unsatisfiable 2.02s 0.51s
% Output : CNFRefutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 25
% Syntax : Number of clauses : 219 ( 219 unt; 0 nHn; 119 RR)
% Number of literals : 219 ( 218 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-2 aty)
% Number of variables : 116 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
eq2(sat_comm(X,Y),bfalse) != btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
sat_comm(X2,Y2) = eq(x(X2,Y2),x(Y2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_020) ).
cnf(c3,plain,
sat_comm(suc(suc(zero)),suc(zero)) = eq(x(suc(suc(zero)),suc(zero)),x(suc(zero),suc(suc(zero)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
rd(cons(i,Xs)) = suc(double(rd(Xs))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_017) ).
cnf(c5,plain,
rd(cons(i,shw(X2))) = suc(double(rd(shw(X2)))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
suc(double(rd(shw(X2)))) = rd(cons(i,shw(X2))),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,axiom,
evenNat(suc(N)) = notb(evenNat(N)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
cnf(c8,plain,
evenNat(suc(zero)) = notb(evenNat(zero)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,axiom,
evenNat(zero) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c10,plain,
notb(evenNat(zero)) = notb(btrue),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,axiom,
notb(btrue) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c12,plain,
notb(evenNat(zero)) = bfalse,
inference(transitivity,[status(thm)],[c10,c11]) ).
cnf(c13,plain,
evenNat(suc(zero)) = bfalse,
inference(transitivity,[status(thm)],[c8,c12]) ).
cnf(c14,plain,
bfalse = evenNat(suc(zero)),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
aux(zero,bfalse) = aux(zero,evenNat(suc(zero))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,axiom,
shw(suc(Y2)) = aux(Y2,evenNat(suc(Y2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
cnf(c17,plain,
shw(suc(zero)) = aux(zero,evenNat(suc(zero))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
aux(zero,evenNat(suc(zero))) = shw(suc(zero)),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
aux(zero,bfalse) = shw(suc(zero)),
inference(transitivity,[status(thm)],[c15,c18]) ).
cnf(c20,plain,
shw(suc(zero)) = aux(zero,bfalse),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
append(shw(suc(zero)),X2) = append(aux(zero,bfalse),X2),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,axiom,
append(cons(Z,Xs2),Y2) = cons(Z,append(Xs2,Y2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
cnf(c23,plain,
append(cons(i,shw(half(suc(X2)))),X3) = cons(i,append(shw(half(suc(X2))),X3)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
cons(i,append(shw(half(suc(X3))),X2)) = append(cons(i,shw(half(suc(X3)))),X2),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,axiom,
aux(Y2,bfalse) = cons(i,shw(half(suc(Y2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
cnf(c26,plain,
aux(X2,bfalse) = cons(i,shw(half(suc(X2)))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
cons(i,shw(half(suc(X2)))) = aux(X2,bfalse),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
append(cons(i,shw(half(suc(X3)))),X2) = append(aux(X3,bfalse),X2),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
cons(i,append(shw(half(suc(X3))),X2)) = append(aux(X3,bfalse),X2),
inference(transitivity,[status(thm)],[c24,c28]) ).
cnf(c30,plain,
cons(i,append(shw(half(suc(zero))),X2)) = append(aux(zero,bfalse),X2),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
append(aux(zero,bfalse),X2) = cons(i,append(shw(half(suc(zero))),X2)),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,axiom,
half(suc(zero)) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c33,plain,
shw(half(suc(zero))) = shw(zero),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
append(shw(half(suc(zero))),X2) = append(shw(zero),X2),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
cons(i,append(shw(half(suc(zero))),X2)) = cons(i,append(shw(zero),X2)),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,axiom,
shw(zero) = nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c37,plain,
append(shw(zero),X2) = append(nil,X2),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
cons(i,append(shw(zero),X2)) = cons(i,append(nil,X2)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,axiom,
append(nil,Y2) = Y2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
cnf(c40,plain,
append(nil,X2) = X2,
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
cons(i,append(nil,X2)) = cons(i,X2),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
cons(i,append(shw(zero),X2)) = cons(i,X2),
inference(transitivity,[status(thm)],[c38,c41]) ).
cnf(c43,plain,
cons(i,append(shw(half(suc(zero))),X2)) = cons(i,X2),
inference(transitivity,[status(thm)],[c35,c42]) ).
cnf(c44,plain,
append(aux(zero,bfalse),X2) = cons(i,X2),
inference(transitivity,[status(thm)],[c31,c43]) ).
cnf(c45,plain,
append(shw(suc(zero)),X2) = cons(i,X2),
inference(transitivity,[status(thm)],[c21,c44]) ).
cnf(c46,plain,
append(shw(suc(zero)),shw(X2)) = cons(i,shw(X2)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
cons(i,shw(X2)) = append(shw(suc(zero)),shw(X2)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
rd(cons(i,shw(X2))) = rd(append(shw(suc(zero)),shw(X2))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,axiom,
x(X2,Y2) = rd(append(shw(X2),shw(Y2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_019) ).
cnf(c50,plain,
x(suc(zero),X2) = rd(append(shw(suc(zero)),shw(X2))),
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
rd(append(shw(suc(zero)),shw(X2))) = x(suc(zero),X2),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
rd(cons(i,shw(X2))) = x(suc(zero),X2),
inference(transitivity,[status(thm)],[c48,c51]) ).
cnf(c53,plain,
suc(double(rd(shw(X2)))) = x(suc(zero),X2),
inference(transitivity,[status(thm)],[c6,c52]) ).
cnf(c54,plain,
x(suc(zero),X2) = suc(double(rd(shw(X2)))),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
double(x(suc(zero),X2)) = double(suc(double(rd(shw(X2))))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
cons(i,X2) = append(shw(suc(zero)),X2),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c57,plain,
cons(o,cons(i,X2)) = cons(o,append(shw(suc(zero)),X2)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,axiom,
half(suc(suc(N2))) = suc(half(N2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
cnf(c59,plain,
half(suc(suc(zero))) = suc(half(zero)),
inference(substitution,[status(thm)],[c58]) ).
cnf(c60,axiom,
half(zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c61,plain,
suc(half(zero)) = suc(zero),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
half(suc(suc(zero))) = suc(zero),
inference(transitivity,[status(thm)],[c59,c61]) ).
cnf(c63,plain,
suc(zero) = half(suc(suc(zero))),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
shw(suc(zero)) = shw(half(suc(suc(zero)))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
append(shw(suc(zero)),X2) = append(shw(half(suc(suc(zero)))),X2),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
cons(o,append(shw(suc(zero)),X2)) = cons(o,append(shw(half(suc(suc(zero)))),X2)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
append(cons(o,shw(half(suc(X3)))),X2) = cons(o,append(shw(half(suc(X3))),X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c68,plain,
cons(o,append(shw(half(suc(X3))),X2)) = append(cons(o,shw(half(suc(X3)))),X2),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,axiom,
aux(Y2,btrue) = cons(o,shw(half(suc(Y2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
cnf(c70,plain,
aux(X2,btrue) = cons(o,shw(half(suc(X2)))),
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
cons(o,shw(half(suc(X2)))) = aux(X2,btrue),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
append(cons(o,shw(half(suc(X3)))),X2) = append(aux(X3,btrue),X2),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
cons(o,append(shw(half(suc(X3))),X2)) = append(aux(X3,btrue),X2),
inference(transitivity,[status(thm)],[c68,c72]) ).
cnf(c74,plain,
cons(o,append(shw(half(suc(suc(zero)))),X2)) = append(aux(suc(zero),btrue),X2),
inference(substitution,[status(thm)],[c73]) ).
cnf(c75,plain,
evenNat(suc(suc(zero))) = notb(evenNat(suc(zero))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c76,plain,
notb(evenNat(suc(zero))) = notb(bfalse),
inference(congruence,[status(thm)],[c13]) ).
cnf(c77,axiom,
notb(bfalse) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c78,plain,
notb(evenNat(suc(zero))) = btrue,
inference(transitivity,[status(thm)],[c76,c77]) ).
cnf(c79,plain,
evenNat(suc(suc(zero))) = btrue,
inference(transitivity,[status(thm)],[c75,c78]) ).
cnf(c80,plain,
btrue = evenNat(suc(suc(zero))),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
aux(suc(zero),btrue) = aux(suc(zero),evenNat(suc(suc(zero)))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
shw(suc(suc(zero))) = aux(suc(zero),evenNat(suc(suc(zero)))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c83,plain,
aux(suc(zero),evenNat(suc(suc(zero)))) = shw(suc(suc(zero))),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
aux(suc(zero),btrue) = shw(suc(suc(zero))),
inference(transitivity,[status(thm)],[c81,c83]) ).
cnf(c85,plain,
append(aux(suc(zero),btrue),X2) = append(shw(suc(suc(zero))),X2),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
cons(o,append(shw(half(suc(suc(zero)))),X2)) = append(shw(suc(suc(zero))),X2),
inference(transitivity,[status(thm)],[c74,c85]) ).
cnf(c87,plain,
cons(o,append(shw(suc(zero)),X2)) = append(shw(suc(suc(zero))),X2),
inference(transitivity,[status(thm)],[c66,c86]) ).
cnf(c88,plain,
cons(o,cons(i,X2)) = append(shw(suc(suc(zero))),X2),
inference(transitivity,[status(thm)],[c57,c87]) ).
cnf(c89,plain,
append(shw(suc(suc(zero))),X2) = cons(o,cons(i,X2)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
rd(append(shw(suc(suc(zero))),X2)) = rd(cons(o,cons(i,X2))),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,axiom,
rd(cons(o,Xs2)) = double(rd(Xs2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_018) ).
cnf(c92,plain,
rd(cons(o,cons(i,X2))) = double(rd(cons(i,X2))),
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
rd(cons(i,X2)) = suc(double(rd(X2))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c94,plain,
double(rd(cons(i,X2))) = double(suc(double(rd(X2)))),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
rd(cons(o,cons(i,X2))) = double(suc(double(rd(X2)))),
inference(transitivity,[status(thm)],[c92,c94]) ).
cnf(c96,plain,
rd(append(shw(suc(suc(zero))),X2)) = double(suc(double(rd(X2)))),
inference(transitivity,[status(thm)],[c90,c95]) ).
cnf(c97,plain,
rd(append(shw(suc(suc(zero))),shw(X2))) = double(suc(double(rd(shw(X2))))),
inference(substitution,[status(thm)],[c96]) ).
cnf(c98,plain,
double(suc(double(rd(shw(X2))))) = rd(append(shw(suc(suc(zero))),shw(X2))),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,plain,
x(suc(suc(zero)),X2) = rd(append(shw(suc(suc(zero))),shw(X2))),
inference(substitution,[status(thm)],[c49]) ).
cnf(c100,plain,
rd(append(shw(suc(suc(zero))),shw(X2))) = x(suc(suc(zero)),X2),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,plain,
double(suc(double(rd(shw(X2))))) = x(suc(suc(zero)),X2),
inference(transitivity,[status(thm)],[c98,c100]) ).
cnf(c102,plain,
double(x(suc(zero),X2)) = x(suc(suc(zero)),X2),
inference(transitivity,[status(thm)],[c55,c101]) ).
cnf(c103,plain,
double(x(suc(zero),suc(zero))) = x(suc(suc(zero)),suc(zero)),
inference(substitution,[status(thm)],[c102]) ).
cnf(c104,plain,
x(suc(suc(zero)),suc(zero)) = double(x(suc(zero),suc(zero))),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
suc(double(rd(shw(suc(zero))))) = x(suc(zero),suc(zero)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c106,plain,
x(suc(zero),suc(zero)) = suc(double(rd(shw(suc(zero))))),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
shw(suc(zero)) = aux(zero,bfalse),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c108,plain,
rd(shw(suc(zero))) = rd(aux(zero,bfalse)),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
rd(cons(o,shw(half(suc(X2))))) = double(rd(shw(half(suc(X2))))),
inference(substitution,[status(thm)],[c91]) ).
cnf(c110,plain,
double(rd(shw(half(suc(X2))))) = rd(cons(o,shw(half(suc(X2))))),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
aux(X2,btrue) = cons(o,shw(half(suc(X2)))),
inference(substitution,[status(thm)],[c69]) ).
cnf(c112,plain,
cons(o,shw(half(suc(X2)))) = aux(X2,btrue),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,plain,
rd(cons(o,shw(half(suc(X2))))) = rd(aux(X2,btrue)),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
double(rd(shw(half(suc(X2))))) = rd(aux(X2,btrue)),
inference(transitivity,[status(thm)],[c110,c113]) ).
cnf(c115,plain,
rd(aux(X2,btrue)) = double(rd(shw(half(suc(X2))))),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
suc(rd(aux(X2,btrue))) = suc(double(rd(shw(half(suc(X2)))))),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
rd(cons(i,shw(half(suc(X2))))) = suc(double(rd(shw(half(suc(X2)))))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c118,plain,
suc(double(rd(shw(half(suc(X2)))))) = rd(cons(i,shw(half(suc(X2))))),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
aux(X2,bfalse) = cons(i,shw(half(suc(X2)))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c120,plain,
cons(i,shw(half(suc(X2)))) = aux(X2,bfalse),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
rd(cons(i,shw(half(suc(X2))))) = rd(aux(X2,bfalse)),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
suc(double(rd(shw(half(suc(X2)))))) = rd(aux(X2,bfalse)),
inference(transitivity,[status(thm)],[c118,c121]) ).
cnf(c123,plain,
suc(rd(aux(X2,btrue))) = rd(aux(X2,bfalse)),
inference(transitivity,[status(thm)],[c116,c122]) ).
cnf(c124,plain,
suc(rd(aux(zero,btrue))) = rd(aux(zero,bfalse)),
inference(substitution,[status(thm)],[c123]) ).
cnf(c125,plain,
rd(aux(zero,bfalse)) = suc(rd(aux(zero,btrue))),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
aux(zero,btrue) = cons(o,shw(half(suc(zero)))),
inference(substitution,[status(thm)],[c69]) ).
cnf(c127,plain,
shw(half(suc(zero))) = shw(zero),
inference(congruence,[status(thm)],[c32]) ).
cnf(c128,plain,
cons(o,shw(half(suc(zero)))) = cons(o,shw(zero)),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
cons(o,shw(zero)) = cons(o,nil),
inference(congruence,[status(thm)],[c36]) ).
cnf(c130,plain,
cons(o,shw(half(suc(zero)))) = cons(o,nil),
inference(transitivity,[status(thm)],[c128,c129]) ).
cnf(c131,plain,
aux(zero,btrue) = cons(o,nil),
inference(transitivity,[status(thm)],[c126,c130]) ).
cnf(c132,plain,
rd(aux(zero,btrue)) = rd(cons(o,nil)),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
suc(rd(aux(zero,btrue))) = suc(rd(cons(o,nil))),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
rd(cons(o,nil)) = double(rd(nil)),
inference(substitution,[status(thm)],[c91]) ).
cnf(c135,plain,
suc(rd(cons(o,nil))) = suc(double(rd(nil))),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,axiom,
rd(nil) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c137,plain,
double(rd(nil)) = double(zero),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
suc(double(rd(nil))) = suc(double(zero)),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,axiom,
double(X2) = addNat(X2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
cnf(c140,plain,
double(zero) = addNat(zero,zero),
inference(substitution,[status(thm)],[c139]) ).
cnf(c141,axiom,
addNat(zero,Y2) = Y2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
cnf(c142,plain,
addNat(zero,zero) = zero,
inference(substitution,[status(thm)],[c141]) ).
cnf(c143,plain,
double(zero) = zero,
inference(transitivity,[status(thm)],[c140,c142]) ).
cnf(c144,plain,
suc(double(zero)) = suc(zero),
inference(congruence,[status(thm)],[c143]) ).
cnf(c145,plain,
suc(double(rd(nil))) = suc(zero),
inference(transitivity,[status(thm)],[c138,c144]) ).
cnf(c146,plain,
suc(rd(cons(o,nil))) = suc(zero),
inference(transitivity,[status(thm)],[c135,c145]) ).
cnf(c147,plain,
suc(rd(aux(zero,btrue))) = suc(zero),
inference(transitivity,[status(thm)],[c133,c146]) ).
cnf(c148,plain,
rd(aux(zero,bfalse)) = suc(zero),
inference(transitivity,[status(thm)],[c125,c147]) ).
cnf(c149,plain,
rd(shw(suc(zero))) = suc(zero),
inference(transitivity,[status(thm)],[c108,c148]) ).
cnf(c150,plain,
double(rd(shw(suc(zero)))) = double(suc(zero)),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
suc(double(rd(shw(suc(zero))))) = suc(double(suc(zero))),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
double(suc(zero)) = addNat(suc(zero),suc(zero)),
inference(substitution,[status(thm)],[c139]) ).
cnf(c153,axiom,
addNat(suc(Z2),Y2) = suc(addNat(Z2,Y2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_014) ).
cnf(c154,plain,
addNat(suc(zero),X2) = suc(addNat(zero,X2)),
inference(substitution,[status(thm)],[c153]) ).
cnf(c155,plain,
addNat(zero,X2) = X2,
inference(substitution,[status(thm)],[c141]) ).
cnf(c156,plain,
suc(addNat(zero,X2)) = suc(X2),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
addNat(suc(zero),X2) = suc(X2),
inference(transitivity,[status(thm)],[c154,c156]) ).
cnf(c158,plain,
addNat(suc(zero),suc(zero)) = suc(suc(zero)),
inference(substitution,[status(thm)],[c157]) ).
cnf(c159,plain,
double(suc(zero)) = suc(suc(zero)),
inference(transitivity,[status(thm)],[c152,c158]) ).
cnf(c160,plain,
suc(double(suc(zero))) = suc(suc(suc(zero))),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
suc(double(rd(shw(suc(zero))))) = suc(suc(suc(zero))),
inference(transitivity,[status(thm)],[c151,c160]) ).
cnf(c162,plain,
x(suc(zero),suc(zero)) = suc(suc(suc(zero))),
inference(transitivity,[status(thm)],[c106,c161]) ).
cnf(c163,plain,
double(x(suc(zero),suc(zero))) = double(suc(suc(suc(zero)))),
inference(congruence,[status(thm)],[c162]) ).
cnf(c164,plain,
double(suc(suc(suc(zero)))) = addNat(suc(suc(suc(zero))),suc(suc(suc(zero)))),
inference(substitution,[status(thm)],[c139]) ).
cnf(c165,plain,
addNat(suc(suc(suc(zero))),X2) = suc(addNat(suc(suc(zero)),X2)),
inference(substitution,[status(thm)],[c153]) ).
cnf(c166,plain,
addNat(suc(suc(zero)),X2) = suc(addNat(suc(zero),X2)),
inference(substitution,[status(thm)],[c153]) ).
cnf(c167,plain,
suc(addNat(suc(zero),X2)) = suc(suc(X2)),
inference(congruence,[status(thm)],[c157]) ).
cnf(c168,plain,
addNat(suc(suc(zero)),X2) = suc(suc(X2)),
inference(transitivity,[status(thm)],[c166,c167]) ).
cnf(c169,plain,
suc(addNat(suc(suc(zero)),X2)) = suc(suc(suc(X2))),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
addNat(suc(suc(suc(zero))),X2) = suc(suc(suc(X2))),
inference(transitivity,[status(thm)],[c165,c169]) ).
cnf(c171,plain,
addNat(suc(suc(suc(zero))),suc(suc(suc(zero)))) = suc(suc(suc(suc(suc(suc(zero)))))),
inference(substitution,[status(thm)],[c170]) ).
cnf(c172,plain,
double(suc(suc(suc(zero)))) = suc(suc(suc(suc(suc(suc(zero)))))),
inference(transitivity,[status(thm)],[c164,c171]) ).
cnf(c173,plain,
double(x(suc(zero),suc(zero))) = suc(suc(suc(suc(suc(suc(zero)))))),
inference(transitivity,[status(thm)],[c163,c172]) ).
cnf(c174,plain,
x(suc(suc(zero)),suc(zero)) = suc(suc(suc(suc(suc(suc(zero)))))),
inference(transitivity,[status(thm)],[c104,c173]) ).
cnf(c175,plain,
eq(x(suc(suc(zero)),suc(zero)),x(suc(zero),suc(suc(zero)))) = eq(suc(suc(suc(suc(suc(suc(zero)))))),x(suc(zero),suc(suc(zero)))),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
suc(double(rd(shw(suc(suc(zero)))))) = x(suc(zero),suc(suc(zero))),
inference(substitution,[status(thm)],[c53]) ).
cnf(c177,plain,
x(suc(zero),suc(suc(zero))) = suc(double(rd(shw(suc(suc(zero)))))),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
shw(suc(suc(zero))) = aux(suc(zero),btrue),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c179,plain,
rd(shw(suc(suc(zero)))) = rd(aux(suc(zero),btrue)),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
double(rd(shw(half(suc(suc(zero)))))) = rd(aux(suc(zero),btrue)),
inference(substitution,[status(thm)],[c114]) ).
cnf(c181,plain,
rd(aux(suc(zero),btrue)) = double(rd(shw(half(suc(suc(zero)))))),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c182,plain,
shw(half(suc(suc(zero)))) = shw(suc(zero)),
inference(congruence,[status(thm)],[c62]) ).
cnf(c183,plain,
rd(shw(half(suc(suc(zero))))) = rd(shw(suc(zero))),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
double(rd(shw(half(suc(suc(zero)))))) = double(rd(shw(suc(zero)))),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
double(rd(shw(suc(zero)))) = double(suc(zero)),
inference(congruence,[status(thm)],[c149]) ).
cnf(c186,plain,
double(rd(shw(suc(zero)))) = suc(suc(zero)),
inference(transitivity,[status(thm)],[c185,c159]) ).
cnf(c187,plain,
double(rd(shw(half(suc(suc(zero)))))) = suc(suc(zero)),
inference(transitivity,[status(thm)],[c184,c186]) ).
cnf(c188,plain,
rd(aux(suc(zero),btrue)) = suc(suc(zero)),
inference(transitivity,[status(thm)],[c181,c187]) ).
cnf(c189,plain,
rd(shw(suc(suc(zero)))) = suc(suc(zero)),
inference(transitivity,[status(thm)],[c179,c188]) ).
cnf(c190,plain,
double(rd(shw(suc(suc(zero))))) = double(suc(suc(zero))),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
suc(double(rd(shw(suc(suc(zero)))))) = suc(double(suc(suc(zero)))),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
double(suc(suc(zero))) = addNat(suc(suc(zero)),suc(suc(zero))),
inference(substitution,[status(thm)],[c139]) ).
cnf(c193,plain,
addNat(suc(suc(zero)),suc(suc(zero))) = suc(suc(suc(suc(zero)))),
inference(substitution,[status(thm)],[c168]) ).
cnf(c194,plain,
double(suc(suc(zero))) = suc(suc(suc(suc(zero)))),
inference(transitivity,[status(thm)],[c192,c193]) ).
cnf(c195,plain,
suc(double(suc(suc(zero)))) = suc(suc(suc(suc(suc(zero))))),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
suc(double(rd(shw(suc(suc(zero)))))) = suc(suc(suc(suc(suc(zero))))),
inference(transitivity,[status(thm)],[c191,c195]) ).
cnf(c197,plain,
x(suc(zero),suc(suc(zero))) = suc(suc(suc(suc(suc(zero))))),
inference(transitivity,[status(thm)],[c177,c196]) ).
cnf(c198,plain,
eq(suc(suc(suc(suc(suc(suc(zero)))))),x(suc(zero),suc(suc(zero)))) = eq(suc(suc(suc(suc(suc(suc(zero)))))),suc(suc(suc(suc(suc(zero)))))),
inference(congruence,[status(thm)],[c197]) ).
cnf(c199,axiom,
eq(suc(X2),suc(Y2)) = eq(X2,Y2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_025) ).
cnf(c200,plain,
eq(suc(suc(suc(suc(suc(suc(zero)))))),suc(suc(suc(suc(suc(zero)))))) = eq(suc(suc(suc(suc(suc(zero))))),suc(suc(suc(suc(zero))))),
inference(substitution,[status(thm)],[c199]) ).
cnf(c201,plain,
eq(suc(suc(suc(suc(suc(zero))))),suc(suc(suc(suc(zero))))) = eq(suc(suc(suc(suc(zero)))),suc(suc(suc(zero)))),
inference(substitution,[status(thm)],[c199]) ).
cnf(c202,plain,
eq(suc(suc(suc(suc(zero)))),suc(suc(suc(zero)))) = eq(suc(suc(suc(zero))),suc(suc(zero))),
inference(substitution,[status(thm)],[c199]) ).
cnf(c203,plain,
eq(suc(suc(suc(zero))),suc(suc(zero))) = eq(suc(suc(zero)),suc(zero)),
inference(substitution,[status(thm)],[c199]) ).
cnf(c204,plain,
eq(suc(suc(zero)),suc(zero)) = eq(suc(zero),zero),
inference(substitution,[status(thm)],[c199]) ).
cnf(c205,axiom,
eq(suc(X2),zero) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_027) ).
cnf(c206,plain,
eq(suc(zero),zero) = bfalse,
inference(substitution,[status(thm)],[c205]) ).
cnf(c207,plain,
eq(suc(suc(zero)),suc(zero)) = bfalse,
inference(transitivity,[status(thm)],[c204,c206]) ).
cnf(c208,plain,
eq(suc(suc(suc(zero))),suc(suc(zero))) = bfalse,
inference(transitivity,[status(thm)],[c203,c207]) ).
cnf(c209,plain,
eq(suc(suc(suc(suc(zero)))),suc(suc(suc(zero)))) = bfalse,
inference(transitivity,[status(thm)],[c202,c208]) ).
cnf(c210,plain,
eq(suc(suc(suc(suc(suc(zero))))),suc(suc(suc(suc(zero))))) = bfalse,
inference(transitivity,[status(thm)],[c201,c209]) ).
cnf(c211,plain,
eq(suc(suc(suc(suc(suc(suc(zero)))))),suc(suc(suc(suc(suc(zero)))))) = bfalse,
inference(transitivity,[status(thm)],[c200,c210]) ).
cnf(c212,plain,
eq(suc(suc(suc(suc(suc(suc(zero)))))),x(suc(zero),suc(suc(zero)))) = bfalse,
inference(transitivity,[status(thm)],[c198,c211]) ).
cnf(c213,plain,
eq(x(suc(suc(zero)),suc(zero)),x(suc(zero),suc(suc(zero)))) = bfalse,
inference(transitivity,[status(thm)],[c175,c212]) ).
cnf(c214,plain,
sat_comm(suc(suc(zero)),suc(zero)) = bfalse,
inference(transitivity,[status(thm)],[c3,c213]) ).
cnf(c215,plain,
eq2(sat_comm(suc(suc(zero)),suc(zero)),bfalse) = eq2(bfalse,bfalse),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,axiom,
eq2(X2,X2) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_029) ).
cnf(c217,plain,
eq2(bfalse,bfalse) = btrue,
inference(substitution,[status(thm)],[c216]) ).
cnf(c218,plain,
eq2(sat_comm(suc(suc(zero)),suc(zero)),bfalse) = btrue,
inference(transitivity,[status(thm)],[c215,c217]) ).
cnf(c219,plain,
$false,
inference(resolution,[status(thm)],[c1,c218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX217-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n002.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 15:13:51 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.02/0.51 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 2.02/0.51
% 2.02/0.51 % SZS status Unsatisfiable
% 2.02/0.51
% 2.02/0.52 % SZS output start CNFRefutation
% See solution above
% 2.37/0.60
% 2.37/0.60 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------